1300 Math Formulas

 

Contents

1 NUMBER SETS

1.1 Set Identities 1

1.2 Sets of Numbers 5

1.3 Basic Identities 7

1.4 Complex Numbers 8

2 ALGEBRA

2.1 Factoring Formulas 12

2.2 Product Formulas 13

2.3 Powers 14

2.4 Roots 15

2.5 Logarithms 16

2.6 Equations 18

2.7 Inequalities 19

2.8 Compound Interest Formulas 22

3 GEOMETRY

3.1 Right Triangle 24

3.2 Isosceles Triangle 27

3.3 Equilateral Triangle 28

3.4 Scalene Triangle 29

3.5 Square 33

3.6 Rectangle 34

3.7 Parallelogram 35

3.8 Rhombus 36

3.9 Trapezoid 37

3.10 Isosceles Trapezoid 38

3.11 Isosceles Trapezoid with Inscribed Circle 40

3.12 Trapezoid with Inscribed Circle 41

3.13 Kite 42

3.14 Cyclic Quadrilateral 43

3.15 Tangential Quadrilateral 45

3.16 General Quadrilateral 46

3.17 Regular Hexagon 47

3.18 Regular Polygon 48

3.19 Circle 50

3.20 Sector of a Circle 53

3.21 Segment of a Circle 54

3.22 Cube 55

3.23 Rectangular Parallelepiped 56

3.24 Prism 57

3.25 Regular Tetrahedron 58

3.26 Regular Pyramid 59

3.27 Frustum of a Regular Pyramid 61

3.28 Rectangular Right Wedge 62

3.29 Platonic Solids 63

3.30 Right Circular Cylinder 66

3.31 Right Circular Cylinder with an Oblique Plane Face 68

3.32 Right Circular Cone 69

3.33 Frustum of a Right Circular Cone 70

3.34 Sphere 72

3.35 Spherical Cap 72

3.36 Spherical Sector 73

3.37 Spherical Segment 74

3.38 Spherical Wedge 75

3.39 Ellipsoid 76

3.40 Circular Torus 78

4 TRIGONOMETRY

4.1 Radian and Degree Measures of Angles 80

4.2 Definitions and Graphs of Trigonometric Functions 81

4.3 Signs of Trigonometric Functions 86

4.4 Trigonometric Functions of Common Angles 87

4.5 Most Important Formulas 88

4.6 Reduction Formulas 89

4.7 Periodicity of Trigonometric Functions 90

4.8 Relations between Trigonometric Functions 90

4.9 Addition and Subtraction Formulas 91

4.10 Double Angle Formulas 92

4.11 Multiple Angle Formulas 93

4.12 Half Angle Formulas 94

4.13 Half Angle Tangent Identities 94

4.14 Transforming of Trigonometric Expressions to Product 95 4.15 Transforming of Trigonometric Expressions to Sum 97

4.16 Powers of Trigonometric Functions 98

4.17 Graphs of Inverse Trigonometric Functions 99

4.18 Principal Values of Inverse Trigonometric Functions 102

4.19 Relations between Inverse Trigonometric Functions 103

4.20 Trigonometric Equations 106

4.21 Relations to Hyperbolic Functions 106

5 MATRICES AND DETERMINANTS

5.1 Determinants 107

5.2 Properties of Determinants 109

5.3 Matrices 110

5.4 Operations with Matrices 111

5.5 Systems of Linear Equations 114

6 VECTORS

6.1 Vector Coordinates 118

6.2 Vector Addition 120

6.3 Vector Subtraction 122

6.4 Scaling Vectors 122

Scalar Product 123 6.6 Vector Product 125

6.5

6.7 Triple Product 127

7 ANALYTIC GEOMETRY

7.1 One -Dimensional Coordinate System 130

7.2 Two -Dimensional Coordinate System 131

7.3 Straight Line in Plane 139

7.4 Circle 149

7.5 Ellipse 152

7.6 Hyperbola 154

7.7 Parabola 158

7.8 Three-Dimensional Coordinate System 161

7.9 Plane 165

7.10 Straight Line in Space 175

7.11 Quadric Surfaces 180

7.12 Sphere 189

8 DIFFERENTIAL CALCULUS

8.1 Functions and Their Graphs 191

8.2 Limits of Functions 208

8.3 Definition and Properties of the Derivative 209

8.4 Table of Derivatives 211

8.5 Higher Order Derivatives 215

8.6 Applications of Derivative 217

8.7 Differential 221

8.8 Multivariable Functions 222

8.9 Differential Operators 225

9 INTEGRAL CALCULUS

9.1 Indefinite Integral 227

9.2 Integrals of Rational Functions 228

9.3 Integrals of Irrational Functions 231

9.4 Integrals of Trigonometric Functions 237

9.5

Integrals of Hyperbolic Functions 241

9.6 Integrals of Exponential and Logarithmic Functions 242

9.7 Reduction Formulas 243

9.8 Definite Integral 247

9.9 Improper Integral 253

9.10 Double Integral 257

9.11 Triple Integral 269

9.12 Line Integral 275

9.13 Surface Integral 285

10 DIFFERENTIAL EQUATIONS

10.1 First Order Ordinary Differential Equations 295

10.2 Second Order Ordinary Differential Equations 298

10.3 Some Partial Differential Equations 302

11 SERIES

11.1 Arithmetic Series 304

11.2 Geometric Series 305

11.3 Some Finite Series 305

11.4 Infinite Series 307

11.5 Properties of Convergent Series 307

11.6 Convergence Tests 308

11.7 Alternating Series 310

11.8 Power Series 311

11.9 Differentiation and Integration of Power Series 312

11.10 Taylor and Maclaurin Series 313

11.11 Power Series Expansions for Some Functions 314

11.12 Binomial Series 316

11.13 Fourier Series 316

12 PROBABILITY

12.1 Permutations and Combinations 318

12.2 Probability Formulas 319